What happens with the quality of sound if I render it twice as MP3?
It boils down to if you are increasing the compression or not, and has nothing to do with Blender.

The reason for this is that any given level of compression will "shape" the encoded values into the compressed shape required. Subsequent compression at the same degree using the same compression technique seeks the exact same shape. Given that the algorithm is seeking the shape the data is already in, very little further degradation will occur typically.

You can test this by trying to encode a JPEG image twice at the same compression level. What you should observe is very little encoded data value shift, and even possibly a growth in file size.

As a general rule, this is a poor option for a pipeline, and it would be much more prudent to keep your interchange data in a lossless and uncompressed format, and encode once and only once. Even expanding an MP3 to a WAV can help you here in theory.